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Proactive Approach for Production and Condition-Based Maintenance Integration Problem in a Deteriorating System

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Abstract

A proactive approach is constructed to cope with the integrated problem of batch production and maintenance in a deteriorating system. The condition of the system is modeled by a proportional hazards model (PHM) which considers both system deterioration state and usage. The deterioration state of system is uncertain and is only observed between batches. An integration model for optimizing production plan and conditionbased maintenance (CBM) policy is proposed, in which the maintenance threshold and production quantity are proactively decided simultaneously. To obtain a robust solution with minimal cost over the planning horizon, a simulation-based iterative algorithm is developed to solve the complicated non-linear model. Numerical results show that the performance of the developed approach is satisfactory under uncertainty.

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Abbreviations

b i, k :

Unit backorder cost of product i in period k

B i, k :

Backorder quantity of product i in period k

c cm :

Cost of a corrective maintenance (CM) action

c c :

Unit production cost of product i in period k

c I :

Cost of an inspection action

c pm :

Cost of a preventive maintenance (PM) action

d d :

Demand of product i in period k

D(t):

System deterioration state as a stochastic variable

E(·):

Expected value

G G :

Max capacity in period k

h(t,D(t)):

Hazard rate function

h h :

Unit inventory holding cost of product i in period k

I I :

Inventory quantity of product i in period k

K K :

Binary variable, which is equal to 1 if a setup is performed for product i in period k, or 0 otherwise

Mc j :

Total maintenance cost in producing batch j

Mt j :

Total maintenance time in producing batch j

N j :

Expected failure times in producing batch j

Pc i,k :

Total production cost in producing product i in period k

Pt i,k :

Total production time in producing product i in period k

Q :

Preventive maintenance threshold

r i,k :

Unit processing time of product i in period k

s i,k :

Unit setup cost of product i in period k

t :

Usage variable

t cm :

Time of a CM action

t j :

Usage before the j-th batch production

t pm :

Time of a PM action

T c :

Total cost over the entire time horizon

u j :

Binary variable, which is equal to 1 if a PM is performed before producing batch j, or 0 otherwise

X i,k :

Production quantity of product i in period k

Z :

Objective function

α, β :

Shape parameter, scale parameter of the gamma process describing D(t)

Γ(·):

Gamma function

δ, λ :

Shape parameter, scale parameter of the Weibull proportional hazards model (PHM)

ΔD(τ):

Increment of D(t) in a period of time τ

θ :

Regression parameter of the Weibull PHM

σ(·):

Standard deviation

i :

Index of product (i = 1, 2,…, P)

j :

Index of continuous batch sequence (j = 1, 2, • • •, PT)

k :

Index of period (k = 1, 2, …, T)

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Authors and Affiliations

  1. School of Mechanical Engineering, Tongji University, Shanghai, 201804, China

    Lin Wang  (王林) & Zhiqiang Lu  (陆志强)

Authors
  1. Lin Wang  (王林)
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  2. Zhiqiang Lu  (陆志强)
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Corresponding author

Correspondence to Zhiqiang Lu  (陆志强).

Additional information

Foundation item: the National Natural Science Foundation of China (Nos. 61473211 and 71171130)

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Wang, L., Lu, Z. Proactive Approach for Production and Condition-Based Maintenance Integration Problem in a Deteriorating System. J. Shanghai Jiaotong Univ. (Sci.) 24, 500–509 (2019). https://doi.org/10.1007/s12204-019-2080-8

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  • DOI: https://doi.org/10.1007/s12204-019-2080-8

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